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it delays checking whether a vertex has been discovered until the vertex is popped from the stack rather than making this check before adding the vertex. If G is a tree, replacing the queue of the breadth-first search algorithm with a stack will yield a depth-first search algorithm. For general graphs, replacing the stack of the iterative depth ...
The vertical line test, shown graphically. The abscissa shows the domain of the (to be tested) function. In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
The Ihara zeta function is defined as the analytic continuation of the infinite product = (),where L(p) is the length of .The product in the definition is taken over all prime closed geodesics of the graph = (,), where geodesics which differ by a cyclic rotation are considered equal.
An example of a problem where this method has been used is the clique problem: given a CNF formula consisting of c clauses, the corresponding graph consists of a vertex for each literal, and an edge between each two non-contradicting [c] literals from different clauses; see the picture. The graph has a c-clique if and only if the formula is ...
Since such graphs have a unique embedding (up to flipping and the choice of the external face), the next bigger graph, if still planar, must be a refinement of the former graph. This allows to reduce the planarity test to just testing for each step whether the next added edge has both ends in the external face of the current embedding.
In computing, data deduplication is a technique for eliminating duplicate copies of repeating data. Successful implementation of the technique can improve storage utilization, which may in turn lower capital expenditure by reducing the overall amount of storage media required to meet storage capacity needs.
The brute force algorithm finds a 4-clique in this 7-vertex graph (the complement of the 7-vertex path graph) by systematically checking all C(7,4) = 35 4-vertex subgraphs for completeness. In computer science , the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called ...